Guillaume Acke

Influence of electron correlation and degeneracy on the Fukui matrix and extension of frontier molecular orbital theory to correlated quantum chemical methods

The Fukui function is considered as the diagonal element of the Fukui matrix in position space, where the Fukui matrix is the derivative of the one particle density matrix (1DM) with respect to the number of electrons. Diagonalization of the Fukui matrix, expressed in an orthogonal orbital basis, explains why regions in space with negative Fukui functions exist. Using a test set of molecules, electron correlation is found to have a remarkable effect on the eigenvalues of the Fukui matrix. The Fukui matrices at the independent electron model level are mathematically proven to always have an eigenvalue equal to exactly unity while the rest of the eigenvalues possibly differ from zero but sum to zero. The loss of idempotency of the 1DM at correlated levels of theory causes the loss of these properties. The influence of electron correlation is examined in detail and the frontier molecular orbital concept is extended to correlated levels of theory by defining it as the eigenvector of the Fukui matrix with the largest eigenvalue. The effect of degeneracy on the Fukui matrix is examined in detail, revealing that this is another way by which the unity eigenvalue and perfect pairing of eigenvalues can disappear.

Can the current density map topology be extracted from the nucleus independent chemical shifts

Aromatic compounds are characterised by the presence of a ring current when in a magnetic field. As a consequence, current density maps are used to assess (the degree of) aromaticity of a compound. However, often a more discrete set of so-called Nucleus Independent Chemical Shift (NICS) values is used that is derived from the current density. It is shown here that there is no simple one-to-one relationship that allows reconstructing current density maps from only NICS-values. NICS values should therefore not be used as aromaticity indices without analysis of the ab initio computed current density map.

Interpreting the behavior of the NICSzz by resolving in orbitals, sign, and positions

The zz component of the nucleus independent chemical shift or the NICSzz is commonly used as a quantifier of the (anti)aromatic character of a (sub)system. One of the underlying assumptions is that a position can be found where the “aromatic” ring currents are adequately reflected in the corresponding NICSzz value. However, as the NICSzz is the result of an integration over the entire space, it no longer explicitly contains the information needed to quantify the separate contributions arising from underlying current density patterns. In this study, we will show that these contributions can be revealed by resolving the NICSzz into orbitals, sign, and positions. Our analysis of benzene in terms of these resolutions shows that the same underlying current density can lead to highly complex shielding patterns that vary greatly depending on the position of the NICSzz ‐probe. As such, our results indicate that any analysis solely based on NICSzz ‐values can lead to results that are difficult to interpret, even if the system under study is considered to be well‐known.

Maximum Probability Domains for Hubbard Models

ABSTRACT The theory of maximum probability domains (MPDs) is formulated for the Hubbard model in terms of projection operators and generating functions for both exact eigenstates as well as Slater determinants. A fast MPD analysis procedure is proposed, which is subsequently used to analyse numerical results for the Hubbard model. It is shown that the essential physics behind the considered Hubbard models can be exposed using MPDs. Furthermore, the MPDs appear to be in line with what is expected from Valence Bond (VB) Theory-based knowledge.

Performance of DFT Methods in Momentum Space: Quantum Similarity Measures versus Moments of Momentum.

The quality of momentum space electron densities obtained from a large array of density functionals is investigated through careful numerical comparison with the density obtained using reference CCSD calculations. Using a test set of 68 closed-shell molecules in their ground state and 77 different computational methods, including coupled cluster, MP2 perturbation theory, Hartree-Fock, and a total of 74 DFT functionals, including long-range corrected functionals, we confirm that DFT momentum densities generally show poorer agreement with the reference than MP2 densities. The performance of DFT functionals varies significantly with only 8 DFT functionals outperforming Hartree-Fock with respect to electron momentum densities and their spherically averaged counterparts.

The influence of correlation on (de)localization indices from a valence bond perspective

AbstractWhen going beyond the Hartree–Fock level to correlated methods, one observes a significant reduction in the delocalization index. This is commonly interpreted as a weakening of electron sharing due to electron correlation, although this is rather counter-intuitive to the concomitant energy lowering. In this study, we use an analytical valence bond model and full CI calculations to show that this reduction in the delocalization index actually goes hand in hand with increased covalent contributions at the expense of ionic contributions. This suggests that we should be careful in formulating interpretations of these results in (de)localization indices. Graphical AbstractVariation of the localization Δ(ΩA, ΩA) and delocalization index Δ(ΩA, ΩB) as a function of the parameter ω. By adjusting this parameter ω from π4

Extended random phase approximation method for atomic excitation energies from correlated and variationally optimized second-order density matrices

\frac {\pi }{4}

Maximum probability domains : theoretical foundations and computational algorithms

to 0, we can gradually change the underlying wave function from a Hartree-Fock to a Heitler-London description.